When making a decision under uncertainty, a Bayesian observer…

Question

BlackTom AI · Accepted Answer

Bayesian decision-making combines prior beliefs with current evidence via Bayes’ theorem, so a Bayesian observer explicitly uses prior knowledge when forming judgments.

1) Relevant knowledge points and concepts:
- Prior: the observer’s belief about states or parameters before seeing current data.
- Likelihood: the probability of observing the current data given each possible state.
- Posterior: the updated belief after combining prior and likelihood, computed by Bayes’ theorem: Posterior ∝ Likelihood × Prior.
- Decision rule: choices often depend on the posterior (e.g., pick the most probable state, or minimize expected loss).

3) Calculation example with intermediate steps:
- Suppose prior P(Disease)=0.01, test sensitivity P(+|Disease)=0.90, false positive rate P(+|NoDisease)=0.05.
- Compute P(+): = 0.01*0.90 + 0.99*0.05 = 0.009 + 0.0495 = 0.0585.
- Compute posterior P(Disease|+): = (0.009) / 0.0585 ≈ 0.1538 (≈15.4%).
This shows the prior (0.01) strongly shapes the posterior even with a positive test.

4) Why the correct answer is correct:
A Bayesian observer does not ignore prior experience; instead the prior is a formal input to the inference process. The posterior combines prior and current information to guide decisions.

5) Why the other options are incorrect:
- "Ignores prior experience.": Opposite of Bayesian principle; priors are central.
- "Only uses the current information available to them.": That describes a purely frequentist or likelihood-only approach, not Bayesian.
- "Ignores any current information available to them.": Ignoring data contradicts Bayesian updating, which multiplies prior by likelihood.

6) Conclusion:
Therefore, the correct answer is "uses their prior knowledge." This matches the provided answer.

When making a decision under uncertainty, a Bayesian observer…单项选择题

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